Question: A few families took a trip to an amusement park together. Tickets cost $$7.50$ each for adults and $$4.50$ each for kids, and the group paid $$42.00$ in total. There were $4$ fewer adults than kids in the group. Find the number of adults and kids on the trip.
Solution: Let $x$ equal the number of adults and $y$ equal the number of kids. The system of equations is then: ${7.5x+4.5y = 42}$ ${x = y-4}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${y-4}$ for $x$ in the first equation. ${7.5}{(y-4)}{+ 4.5y = 42}$ Simplify and solve for $y$ $ 7.5y-30 + 4.5y = 42 $ $ 12y-30 = 42 $ $ 12y = 72 $ $ y = \dfrac{72}{12} $ ${y = 6}$ Now that you know ${y = 6}$ , plug it back into ${x = y-4}$ to find $x$ ${x = }{(6)}{ - 4}$ ${x = 2}$ You can also plug ${y = 6}$ into ${7.5x+4.5y = 42}$ and get the same answer for $x$ ${7.5x + 4.5}{(6)}{= 42}$ ${x = 2}$ There were $2$ adults and $6$ kids.